




'''simple docstring'''


class  __lowercase    :







   def __init__(						self   ,				UpperCamelCase   ,				UpperCamelCase   ,				UpperCamelCase   )					->     Optional[Any]:
     __a								=       None
     __a								=       None
     __a								=       graph

     self._normalize_graph(UpperCamelCase   ,				UpperCamelCase   )
     __a								=       len(UpperCamelCase   )
     __a								=       None







   def 		UpperCamelCase__      (						self   ,				UpperCamelCase   ,				UpperCamelCase   )					->     str:
     if sources is int:
       __a								=       [sources]
     if sinks is int:
       __a								=       [sinks]

     if len(UpperCamelCase   ) == 0 or len(UpperCamelCase   ) == 0:
       return

     __a								=       sources[0]
     __a								=       sinks[0]

     # make fake vertex if there are more
     # than one source or sink
     if len(UpperCamelCase   ) > 1 or len(UpperCamelCase   ) > 1:
       __a								=       0
       for i in sources:
         max_input_flow += sum(self.graph[i]   )

       __a								=       len(self.graph   ) + 1
       for room in self.graph:
         room.insert(0   ,				0   )
       self.graph.insert(0   ,				[0] * size   )
       for i in sources:
         __a								=       max_input_flow
       __a								=       0

       __a								=       len(self.graph   ) + 1
       for room in self.graph:
         room.append(0   )
       self.graph.append([0] * size   )
       for i in sinks:
         __a								=       max_input_flow
       __a								=       size - 1







   def 		UpperCamelCase__      (						self   )					->     Any:
     if self.maximum_flow_algorithm is None:
       raise Exception('You need to set maximum flow algorithm before.'   )
     if self.source_index is None or self.sink_index is None:
       return 0

     self.maximum_flow_algorithm.execute()
     return self.maximum_flow_algorithm.getMaximumFlow()







   def 		UpperCamelCase__      (						self   ,				UpperCamelCase   )					->     Union[str, Any]:
     __a								=       algorithm(self   )





class  __lowercase    :







   def __init__(						self   ,				UpperCamelCase   )					->     Union[str, Any]:
     __a								=       flow_network
     __a								=       flow_network.verticesCount
     __a								=       flow_network.sourceIndex
     __a								=       flow_network.sinkIndex
     # it's just a reference, so you shouldn't change
     # it in your algorithms, use deep copy before doing that
     __a								=       flow_network.graph
     __a								=       False







   def 		UpperCamelCase__      (						self   )					->     Any:
     if not self.executed:
       self._algorithm()
       __a								=       True







   def 		UpperCamelCase__      (						self   )					->     Any:
     pass





class  __lowercase    (	__magic_name__			):







   def __init__(						self   ,				UpperCamelCase   )					->     Optional[int]:
     super().__init__(UpperCamelCase   )
     # use this to save your result
     __a								=       -1







   def 		UpperCamelCase__      (						self   )					->     int:
     if not self.executed:
       raise Exception('You should execute algorithm before using its result!'   )

     return self.maximum_flow





class  __lowercase    (	__magic_name__			):







   def __init__(						self   ,				UpperCamelCase   )					->     Any:
     super().__init__(UpperCamelCase   )

     __a								=       [[0] * self.verticies_count for i in range(self.verticies_count   )]

     __a								=       [0] * self.verticies_count
     __a								=       [0] * self.verticies_count







   def 		UpperCamelCase__      (						self   )					->     Optional[int]:
     __a								=       self.verticies_count

     # push some substance to graph
     for nextvertex_index, bandwidth in enumerate(self.graph[self.source_index]   ):
       self.preflow[self.source_index][nextvertex_index] += bandwidth
       self.preflow[nextvertex_index][self.source_index] -= bandwidth
       self.excesses[nextvertex_index] += bandwidth

     # Relabel-to-front selection rule
     __a								=       [
         i
         for i in range(self.verticies_count   )
         if i != self.source_index and i != self.sink_index
     ]

     # move through list
     __a								=       0
     while i < len(UpperCamelCase   ):
       __a								=       vertices_list[i]
       __a								=       self.heights[vertex_index]
       self.process_vertex(UpperCamelCase   )
       if self.heights[vertex_index] > previous_height:
         # if it was relabeled, swap elements
         # and start from 0 index
         vertices_list.insert(0   ,				vertices_list.pop(UpperCamelCase   )   )
         __a								=       0
       else:
         i += 1

     __a								=       sum(self.preflow[self.source_index]   )







   def 		UpperCamelCase__      (						self   ,				UpperCamelCase   )					->     Optional[Any]:
     while self.excesses[vertex_index] > 0:
       for neighbour_index in range(self.verticies_count   ):
         # if it's neighbour and current vertex is higher
         if (
             self.graph[vertex_index][neighbour_index]
             - self.preflow[vertex_index][neighbour_index]
             > 0
             and self.heights[vertex_index] > self.heights[neighbour_index]
         ):
           self.push(UpperCamelCase   ,				UpperCamelCase   )

       self.relabel(UpperCamelCase   )







   def 		UpperCamelCase__      (						self   ,				UpperCamelCase   ,				UpperCamelCase   )					->     List[str]:
     __a								=       min(
         self.excesses[from_index]   ,				self.graph[from_index][to_index] - self.preflow[from_index][to_index]   ,				)
     self.preflow[from_index][to_index] += preflow_delta
     self.preflow[to_index][from_index] -= preflow_delta
     self.excesses[from_index] -= preflow_delta
     self.excesses[to_index] += preflow_delta







   def 		UpperCamelCase__      (						self   ,				UpperCamelCase   )					->     Tuple:
     __a								=       None
     for to_index in range(self.verticies_count   ):
       if (
           self.graph[vertex_index][to_index]
           - self.preflow[vertex_index][to_index]
           > 0
       ) and (min_height is None or self.heights[to_index] < min_height):
         __a								=       self.heights[to_index]

     if min_height is not None:
       __a								=       min_height + 1


if __name__ == "__main__":
  UpperCAmelCase_					=   [0]
  UpperCAmelCase_					=   [3]
  # graph = [
  #     [0, 0, 4, 6, 0, 0],
  #     [0, 0, 5, 2, 0, 0],
  #     [0, 0, 0, 0, 4, 4],
  #     [0, 0, 0, 0, 6, 6],
  #     [0, 0, 0, 0, 0, 0],
  #     [0, 0, 0, 0, 0, 0],
  # ]
  UpperCAmelCase_					=   [[0, 7, 0, 0], [0, 0, 6, 0], [0, 0, 0, 8], [9, 0, 0, 0]]

  # prepare our network
  UpperCAmelCase_					=   FlowNetwork(graph, entrances, exits)
  # set algorithm
  flow_network.set_maximum_flow_algorithm(PushRelabelExecutor)
  # and calculate
  UpperCAmelCase_					=   flow_network.find_maximum_flow()

  print(f"""maximum flow is {maximum_flow}""")









'''simple docstring'''


from typing import TYPE_CHECKING

from ...utils import (
    OptionalDependencyNotAvailable,
    _LazyModule,
    is_sentencepiece_available,
    is_tokenizers_available,
    is_torch_available,
)


UpperCAmelCase_					=   {"configuration_fnet": ["FNET_PRETRAINED_CONFIG_ARCHIVE_MAP", "FNetConfig"]}

try:
  if not is_sentencepiece_available():
    raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
  pass
else:
  UpperCAmelCase_					=   ["FNetTokenizer"]

try:
  if not is_tokenizers_available():
    raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
  pass
else:
  UpperCAmelCase_					=   ["FNetTokenizerFast"]

try:
  if not is_torch_available():
    raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
  pass
else:
  UpperCAmelCase_					=   [
      "FNET_PRETRAINED_MODEL_ARCHIVE_LIST",
      "FNetForMaskedLM",
      "FNetForMultipleChoice",
      "FNetForNextSentencePrediction",
      "FNetForPreTraining",
      "FNetForQuestionAnswering",
      "FNetForSequenceClassification",
      "FNetForTokenClassification",
      "FNetLayer",
      "FNetModel",
      "FNetPreTrainedModel",
  ]


if TYPE_CHECKING:
  from .configuration_fnet import FNET_PRETRAINED_CONFIG_ARCHIVE_MAP, FNetConfig

  try:
    if not is_sentencepiece_available():
      raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
    pass
  else:
    from .tokenization_fnet import FNetTokenizer

  try:
    if not is_tokenizers_available():
      raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
    pass
  else:
    from .tokenization_fnet_fast import FNetTokenizerFast

  try:
    if not is_torch_available():
      raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
    pass
  else:
    from .modeling_fnet import (
        FNET_PRETRAINED_MODEL_ARCHIVE_LIST,
        FNetForMaskedLM,
        FNetForMultipleChoice,
        FNetForNextSentencePrediction,
        FNetForPreTraining,
        FNetForQuestionAnswering,
        FNetForSequenceClassification,
        FNetForTokenClassification,
        FNetLayer,
        FNetModel,
        FNetPreTrainedModel,
    )


else:
  import sys

  UpperCAmelCase_					=   _LazyModule(__name__, globals()["__file__"], _import_structure, module_spec=__spec__)



